Question: Rewrite as a simplified fraction. ${0.5\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 53.3333...\\ 10x &= 5.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 48}$ ${x = \dfrac{48}{90}} $ ${x = \dfrac{8}{15}} $